Previous Geometry Festival Speakers

1985 at Penn:

• Marcel Berger
• Pat Eberlein
• Jost Eschenburg
• Friedrich Hirzebruch
• Blaine Lawson
• Leon Simon
• Scott Wolpert
• Deane Yang

1986 at Maryland:

• Uwe Abresch, "Explicit constant mean curvature tori"
• Zhi-yong Gao, "The existence of negatively Ricci curved metrics"
• David Hoffman, "New results in the global theory of minimal surfaces"
• Jack Lee, "Conformal geometry and the Yamabe problem"
• Ngai-ming Mok, "Compact K�hler manifolds of non-negative curvature"
• John Morgan, "Self dual connections and the topology of 4-manifolds"
• Chuu-lian Terng, "Submanifolds with flat normal bundle"

1987 at Penn:

• Robert Bryant, "The construction of metrics with exceptional holonomy"
• Francis Bonahon, "Hyperbolic 3-manifolds with arbitrarily short geodesics"
• Keith Burns, "Geodesic flows on the 2-sphere"
• Andreas Floer, "Instantons and Casson's invariant"
• Hermann Karcher, "Embedded minimal surfaces in the 3-sphere"
• J�rgen Moser, "Minimal foliations of tori"
• Ed Witten. "Applications of quantum field theory to topology"

1988 at North Carolina:

• Detlef Gromoll, "On complete spaces of non-negative Ricci curvature"
• Nicolas Kapouleas, "Constant mean curvature surfaces in E³"
• Robert Osserman, "Gauss map of complete minimal surfaces"
• Pierre Pansu, "L^p-cohomology of negatively curved manifolds"
• Peter Petersen, "Bounding homotopy types by geometry"
• Gang Tian, "K�hler-Einstein metrics on quasiprojective manifolds"
• DaGang Yang, "Some new examples of manifolds of positive Ricci curvature"
• Wolfgang Ziller, "Recent results on Einstein metrics"

1989 at Stony Brook:

• Eugenio Calabi, "Extremal singular metrics on surfaces"
• Harold Donnelly, "Nodal sets of eigenfunctions on Riemannian manifolds"
• Yasha Eliashberg, "Symplectic geometric methods in several complex variables"
• Thomas Farrell, "A topological analogue of Mostow's rigidity theorem"
• Lesley Sibner, "Solutions to Yang-Mills equations which are not self-dual"
• Carlos Simpson, "Moduli spaces of representations of fundamental groups"

1990 at Maryland:

• Michael T. Anderson, "Behavior of metrics under Ricci curvature bounds"
• Kevin Corlette, "Harmonic maps and geometric superrigidity"
• Kenji Fukaya, "Fundamental groups of almost non-negatively curved manifolds"
• Misha Gromov, "Recent progress in symplectic geometry"
• Werner M�ller, "On spectral theory for locally symmetric manifolds with finite volume"
• Rick Schoen, "Least area problems for Lagrangian submanifolds"
• Gudlaugur Thorbergsson, "Isoparametric submanifolds and their Tits buildings"
• Shing-Tung Yau, "Some theorems in K�hler geometry"

1991 at Duke:

• Jeff Cheeger, "Transgressed Euler classes of SL(2n,Z)-bundles and adiabatic limits of eta-invariants"
• Chris Croke, "Volumes of balls in manifolds without conjugate points and rigidity of geodesic flows"
• Carolyn Gordon, "When you can't hear the shape of a manifold"
• Wu-Yi Hsiang, "Sphere packing and spherical geometry: The Kepler conjecture and beyond"
• Alan Nadel, "On the geometry of Fano varieties"
• Grigori Perelman, "Alexandrov's spaces with curvature bounded from below"
• Stefan Stolz, "On the space of positive curvature metrics modulo diffeomorphisms"

1992 at Courant:

• Jonathan Block, "Aperiodic tilings, positive scalar curvature and other homological phenomena"
• John Franks, "Infinitely many closed geodesics on the 2-sphere"
• Karsten Grove, "The inevitable presence of singular spaces in Riemannian geometry"
• Lisa Jeffrey, "Volumes of moduli spaces of flat connections on Riemannian surfaces"
• Jun Li, "Anti-self-dual connections on SU(2) bundles over algebraic surfaces"
• Dusa McDuff, "Symplectic 4-manifolds"
• Clifford Taubes, "Anti-self dual conformal structures in 4 dimensions"

1993 at Penn:

• Shing-Shen Chern, "Finsler geometry"
• Richard Hamilton, "An isoperimetric estimate for the curve-shrinking flow"
• Vaughan Jones, "Loop groups and operator algebras"
• Claude LeBrun, "Compact K�hler manifolds of constant scalar curvature"
• Louis Nirenberg, "The maximum principle and related things"
• Xiaochun Rong, "Collapsing in low dimensions and rationality of geometric invariants"
• I. M. Singer, "Geometry and quantum field theory"

1995 at Stony Brook:

• Dimitri Burago, "Asymptotic geometry of Zⁿ-periodic metrics"
• Tobias Colding, "Ricci curvature and convergence"
• Dominic Joyce, "Compact Riemannian manifolds with exceptional holonomy groups"
• Yael Karshon, "Hamiltonian torus actions"
• David Morrison, "Analogues of Seiberg-Witten invariants for counting curves on Calabi-Yau manifolds"
• Tom Mrowka, "The Seiberg-Witten equations and 4-manifold topology"
• Yongbin Ruan, "Higher genus pseudo-holomorphic curves"
• Edward Witten, "Monopoles and four-manifolds"

1996 at Maryland:

• J. Baez, "Quantum gravity and BF theory in 4 dimensions"
• Jean-Luc Brylinski, "Gauge groups and reciprocity laws on algebraic varieties"
• Bruce Kleiner, "Spaces of nonpositive curvature"
• G. Margulis, "Quantitative Oppenheim Conjecture"
• S. P. Novikov, "Laplace and Darboux transformations"
• Richard Schwartz, "The Devil's Pentagram"
• Guofong Wei, "Volume comparison with integral curvature bounds"
• Shmuel Weinberger, "Equivariant rigidity: For and against"

1997 at Duke:

• Jeanne Nielsen Clelland , "Geometry of Conservation Laws for Parabolic PDE's"
• Anatole Katok , "Rigidity and invariant geometric structures for differentiable group actions"
• Fran�ois Labourie , "Monge-Ampere problems, holomorphic curves and laminations"
• Gang Liu, "Floer Homology and the Arnold Conjecture"
• William Minicozzi, "Harmonic functions on manifolds"
• Lorenz Schwachh�fer, "The classification of irreducible holonomies of torsion free connections"
• Matthias Schwarz, "Symplectic fixed points and quantum cohomology"
• Stephen Semmes, "Geometry with little smoothness"

1998 at Stony Brook:

• Scott Axelrod, "Generalized Chern-Simons invariants as a generalized Lagrangian field theory"
• Jean-Michel Bismut, "Chern-Simons classes, Bott Chern classes and analytic torsion"
• Spencer Bloch, "Algebro-geometric Chern-Simons classes"
• Robert Bryant, "Recent progress on the holonomy classification problem"
• Robert Bryant (for S.-S. Chern), "Recent results and open problems in Finsler geometry"
• Jeff Cheeger and Blaine Lawson, "The mathematical work of James Simons"
• Jeff Cheeger, "Ricci Curvature"
• J�rg Fr�hlich, "Physics and the Chern-Simons form (from anomalies to the quantum Hall effect to magnetic stars)"
• Mikhail Gromov, "Dynamics on function spaces"
• Maxim Kontsevich, "On regulators, critical values and q-factorials"
• Blaine Lawson, "Connections and singularities of maps"
• Robert MacPherson, "Spaces with torus actions"
• John Milnor, "Remarks on geometry and dynamics"
• I.M. Singer, TBA
• Dennis Sullivan "A combinatorial model for non-linearity"
• Clifford Taubes, "Seiberg-Witten invariants, harmonic forms, and their pseudo-holomorphic curves"
• Gang Tian, "Yang-Mills connections and calibration"
• C.-N. Yang, "Vector potentials and connections"
• S.-T. Yau, "Mirror symmetry and rational curves"

1999 at Penn:

• Peter Sarnak, "Some spectral problems on negatively curved manifolds"
• Zheng-xu He, "The gradient flow for the M�bius energy of knots"
• Curtis McMullen, "The moduli space of Riemann surfaces is K�hler-hyperbolic"
• Paul Biran, "Lagrange skeletons and symplectic rigidity"
• Helmut Hofer, Holomorphic curves and contact geometry"
• Werner Ballmann, "On negative curvature and the essential spectrum of geometric operators"
• Shlomo Sternberg, "Multiplets of representations and Kostant's Dirac operator"

2000 at Maryland:

• Samuel Ferguson, "The Kepler Conjecture"
• Robert Meyerhoff, "Rigorous computer-aided proofs in the theory of hyperbolic 3-manifolds"
• Herman Gluck, "Geometry, topology and plasma physics"
• Burkhard Wilking, "New examples of manifolds with positive sectional curvature almost everywhere"
• John Roe, "Amenability and assembly maps"
• Eleny Ionel, "Gromov invariants of symplectic sums"
• Mikhail Gromov, "Spaces of holomorphic maps"

2001 at Northeastern:

• Robert Bryant, "Rigidity and quasirigidity of extremal cycles in Hermitian symmetric spaces"
• Tobias Colding, "Embedded minimal surfaces in 3-manifolds"
• Boris Dubrovin, "Normal forms of integrable PDE's"
• John Lott, "Heat equation methods in noncommutative geometry"
• Dusa McDuff, "Seminorms on the Hamiltonian group and the nonsqueezing theorem"
• Rick Schoen, "Variational approaches to the construction minimal lagrangian submanifolds"
• Shing-Tung Yau, "Mirror symmetry"

2002 at Courant:

• Denis Auroux, "Singular plane curves and topological invariants of symplectic manifolds"
• Hugh Bray, "On the mass of higher dimensional black holes"
• Alice Chang, "Conformally invariant operators and the Gauss-Bonnet integrand"
• Xiuxiong Chen,"The space of K�hler metrics"
• George Daskalopoulos,"On the Yang-Mills flow in higher dimensions"
• Alex Eskin, "Billiards and lattices"
• Juha Heinonen, "On the existence of quasiregular mappings"

2003 at Duke:

• Bennett Chow, "Harnack estimates of Li-Yau-Hamilton type for the Ricci flow"
• Anda Degeratu, "Geometrical McKay Correspondance"
• Ron Donagi, "Griffiths' intermediate Jacobians, integrable systems, and string theory"
• John Etnyre, "Legendrian knots in high dimensions"
• Joe Harris, "Are Cubics Rational?"
• Claude LeBrun, "Zoll Manifolds, Complex Surfaces, and Holomorphic Disks"
• John Morgan, "Variations of Hodge structure for 1-parameter families of Calabi-Yau three-folds"
• Madhav Nori, "A modified Hodge conjecture"
• Justin Sawon, "Twisted Fourier-Mukai transforms for holomorphic symplectic manifolds"
• Wilfried Schmid, "Automorphic distributions, L-functions, and functional equations"
• Jeff Viaclovsky, "Fully nonlinear equations and conformal geometry"
• Claire Voisin, "K-correspondences and intrinsic pseudovolume forms"

2004 at Courant:

• Jean-Michel Bismut, "The Hypoelliptic Laplacian on the Cotangent Bundle"
• Yasha Eliashberg, "Positive Loops of Contact Transformations"
• Blaine Lawson, "Projective Hulls and the Projective Gelfand Transformation"
• Dusa McDuff, "Applications of J-holomorphic Curves"
• Xiaochun Rong, "Local splitting structures on nonpositively curved manifolds"
• Dennis Sullivan, "Algebraic topology in string backgrounds"
• Gang Tian, "Extremal Metrics and Holomorphic Discs"
• Edward Witten, "Gauge Theory Scattering From Curves In CP³"

2005 at Stony Brook:

• Nancy Hingston, "Periodic solutions of Hamilton's equations on tori"
• Sergiu Klainerman, "Null hypersurfaces and curvature estimates in general relativity"
• Bruce Kleiner, "Singular structure of mean curvature flow"
• Frank Pacard, "Blowing up Kahler manifolds with constant scalar curvature"
• Rahul Pandharipande, "A topological view of Gromov-Witten theory"
• Igor Rodniansky, "Non-linear waves and Einstein geometry"
• Yum-Tong Siu, "Methods of singular metrics in algebraic geometry"
• Katrin Wehrheim, "Floer theories in symplectic topology and gauge theory"

2006 at Penn:

• Jeff Cheeger, "Differentiation, bi-Lipschitz nonembedding and embedding"
• Charles Fefferman, "Fitting a smooth function to data"
• Helmut Hofer, "On the analytic and geometric foundations of symplectic field theory"
• Ko Honda, "Reeb vector fields and open book decompositions"
• William Meeks, "The Dynamics Theorem for embedded minimal surfaces"
• Yair Minsky, "Asymptotic geometry of the mapping class group"
• Frank Morgan, "Manifolds with Density"
• Zoltan Szabo, "Link Floer homology and the Thurston norm"

2007 at Maryland:

• Dan Freed, "Secondary differential-geometric invariants, generalized cohomology, and QCD"
• Xiaobo Lu, "Mean curvature flow for isoparametric submanifolds"
• Vitali Kapovith, "Some open problems in comparison geometry"
• Maryam Mirzakhani, Lattice point asymptotics and conformal densities on Teichm�ller space
• Charles Epstein, "Stein fillings and index theorems"
• Guoliang Yu, "Group actions and K-theory"
• Simon Brendle, "Blow-up phenomena for the Yamabe PDE in high dimensions"

2008 at Duke:

• Michael Anderson, "Conformally compact Einstein metrics with prescribed conformal infinity"
• Robert Bryant,"Riemannian Submersions as PDE"
• Greg Galloway, "Stability of marginally trapped surfaces with applications to black holes"
• Marcus Khuri, "The Yamabe Problem Revisited"
• John Lott, "Optimal transport in Riemannian geometry and Ricci flow"
• William Minicozzi, "The rate of change of width under flows"
• Duong Phong, "Stability and constant scalar curvature"
• Jeff Viaclovsky, "Orthogonal Complex Structures"